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Addition of Polynomials

State whether...

Question

State whether True or False.
Multiply: $2 y - 4 y^{3} + 6 y^{5}$ by $y^{2} + y - 3$ .
The answer is $6 y^{7} + 6 y^{6} - 22 y^{5} - 4 y^{4} + 14 y^{3} + 2 y^{2} - 6 y$ .

A

True

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B

False

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Solution

The correct option is A True
$(2 y - 4 y^{3} + 6 y^{5}) \times (y^{2} + y - 3)$
$= (2 y - 4 y^{3} + 6 y^{5}) y^{2} + (2 y - 4 y^{3} + 6 y^{5}) y - 3 (2 y - 4 y^{3} + 6 y^{5})$
$= 2 y^{3} - 4 y^{5} + 6 y^{7} + 2 y^{2} - 4 y^{4} + 6 y^{6} - 6 y + 12 y^{3} - 18 y^{5}$
$= 6 y^{7} + 6 y^{6} - 22 y^{5} - 4 y^{4} + 14 y^{3} + 2 y^{2} - 6 y$

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